Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
298 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C5×#131⋊C3 | C4 | semidirect |
| 7. C5×GU(2,𝔽3) | C4 | semidirect |
| 8. C5×#859 | C4 | semidirect |
| 10. #73121 | C5 | direct (N × H) |
| 29. C5×#131 | Dic3 | semidirect |
| 50. #131⋊C3 | C4×C5 | semidirect |
| 51. GU(2,𝔽3) | C4×C5 | semidirect |
| 52. #859 | C4×C5 | semidirect |
| 117. #131 | C5×Dic3 | semidirect |
| 203. C5 | #73121 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#131⋊C3 | 2 |
| C5×#5424 | 2 |
| C2×C5×GU(2,𝔽3) | 2 |
| C5×#1764 | 3 |
| C5×C8×Dic3 | 4 |
| #73121 | 5 |